Top-quark mass effects in double and triple Higgs production in gluon-gluon fusion at NLO

TL;DR

The paper tackles the challenge of accurate predictions for double and triple Higgs production via gluon-gluon fusion, where top-quark mass and width effects in loops are non-negligible. It introduces a reweighting method that starts from HEFT-based NLO+PS events and incorporates exact top-quark mass and width information from one- and two-loop amplitudes (via the FT_approx scheme), enabling better predictions for HH and HHH. The authors find that including exact real-emission amplitudes is crucial for high-pT regions and that remaining uncertainties from unknown two-loop virtuals are about 10%. They deliver first NLO+PS predictions for HHH and demonstrate reduced theoretical uncertainties, providing a robust framework for improved multi-Higgs phenomenology at hadron colliders.

Abstract

The observation of double and triple scalar boson production at hadron colliders could provide key information on the Higgs self couplings and the potential. As for single Higgs production the largest rates for multiple Higgs production come from gluon-gluon fusion processes mediated by a top-quark loop. However, at variance with single Higgs production, top-quark mass and width effects from the loops cannot be neglected. Computations including the exact top-quark mass dependence are only available at the leading order, and currently predictions at higher orders are obtained by means of approximations based on the Higgs-gluon effective field theory (HEFT). In this work we present a reweighting technique that, starting from events obtained via the MC@NLO method in the HEFT, allows to exactly include the top-quark mass and width effects coming from one- and two-loop amplitudes. We describe our approach and apply it to double Higgs production at NLO in QCD, computing the needed one-loop amplitudes and using approximations for the unknown two-loop ones. The results are compared to other approaches used in the literature, arguing that they provide more accurate predictions for distributions and for total rates as well. As a novel application of our procedure we present predictions at NLO in QCD for triple Higgs production at hadron colliders.

Figures (8)

• Figure 1: Representative Feynman diagrams for box and triangle topologies for Higgs pair production in gluon-gluon fusion at the lowest order in perturbative QCD. The two gauge-indepedent classes of diagrams interfere destructively.
• Figure 2: Sample of Feynman diagrams for the NLO Higgs pair production in gluon-gluon fusion. a) Real one-loop and b) virtual two-loop corrections.
• Figure 3: Top width effect on the one-loop (Born) matrix element squared for $g g \rightarrow H H$. The results for $\Gamma_t=0$ and 1.5 GeV are shown along with the corresponding ratio.
• Figure 4: Differential cross sections for the invariant mass and transverse momentum of the Higgs pair in $HH$ production via gluon-gluon fusion at the LHC with 14 TeV centre-of-mass energy. Distributions are obtained by generating events at parton level at LO and NLO accuracy and then matching to Pythia8. Uncertainties corresponding to PDF and scale variations are shown in the lower inset.
• Figure 5: Total cross sections at LO and NLO in QCD in the FT for the Higgs pair production from gluon-gluon fusion at $pp$ colliders as a function of the centre-of-mass energy. The thickness of the lines corresponds to the scale variation and PDF uncertainties added linearly.